{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Phase Relative Permeability correlations \n",
    "\n",
    "> Divyanshu Vyas | Oil & Gas Data Science/Machine Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 1 :  Wyllie and Gardner method\n",
    "Generate the drainage relative permeability data for an **unconsolidated\n",
    "well-sorted sand**. Assume the\n",
    "following critical saturation values:\n",
    "\n",
    "> Soc = 0.3, Swc = 0.25, Sgc = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "sw = np.linspace(0.25,0.70,100)\n",
    "\n",
    "Swc = 0.25\n",
    "\n",
    "Soc = 0.3\n",
    "\n",
    "Sgc = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_wg = pd.DataFrame(data=sw , columns=['Sw'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_wg['Sw*'] = (df_wg['Sw'] - Swc)/(1-Swc)\n",
    "\n",
    "df_wg['Kro'] = (1 - df_wg['Sw*'])**3\n",
    "\n",
    "df_wg['Krw'] = df_wg['Sw*']**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sw</th>\n",
       "      <th>Sw*</th>\n",
       "      <th>Kro</th>\n",
       "      <th>Krw</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.250000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.254545</td>\n",
       "      <td>0.006061</td>\n",
       "      <td>0.981928</td>\n",
       "      <td>2.226118e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.259091</td>\n",
       "      <td>0.012121</td>\n",
       "      <td>0.964075</td>\n",
       "      <td>1.780894e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.263636</td>\n",
       "      <td>0.018182</td>\n",
       "      <td>0.946440</td>\n",
       "      <td>6.010518e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.268182</td>\n",
       "      <td>0.024242</td>\n",
       "      <td>0.929022</td>\n",
       "      <td>1.424715e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>0.681818</td>\n",
       "      <td>0.575758</td>\n",
       "      <td>0.076356</td>\n",
       "      <td>1.908618e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.686364</td>\n",
       "      <td>0.581818</td>\n",
       "      <td>0.073130</td>\n",
       "      <td>1.969527e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.690909</td>\n",
       "      <td>0.587879</td>\n",
       "      <td>0.069996</td>\n",
       "      <td>2.031718e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.695455</td>\n",
       "      <td>0.593939</td>\n",
       "      <td>0.066953</td>\n",
       "      <td>2.095204e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.600000</td>\n",
       "      <td>0.064000</td>\n",
       "      <td>2.160000e-01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Sw       Sw*       Kro           Krw\n",
       "0   0.250000  0.000000  1.000000  0.000000e+00\n",
       "1   0.254545  0.006061  0.981928  2.226118e-07\n",
       "2   0.259091  0.012121  0.964075  1.780894e-06\n",
       "3   0.263636  0.018182  0.946440  6.010518e-06\n",
       "4   0.268182  0.024242  0.929022  1.424715e-05\n",
       "..       ...       ...       ...           ...\n",
       "95  0.681818  0.575758  0.076356  1.908618e-01\n",
       "96  0.686364  0.581818  0.073130  1.969527e-01\n",
       "97  0.690909  0.587879  0.069996  2.031718e-01\n",
       "98  0.695455  0.593939  0.066953  2.095204e-01\n",
       "99  0.700000  0.600000  0.064000  2.160000e-01\n",
       "\n",
       "[100 rows x 4 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_wg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('default')\n",
    "\n",
    "plt.plot(df_wg['Sw'] , df_wg['Kro'], lw=3.5,label ='Kro')\n",
    "plt.plot(df_wg['Sw'] , df_wg['Krw'], lw=3.5,label='Krw')\n",
    "\n",
    "# plt.xlim(0,1)\n",
    "\n",
    "plt.xlabel('Sw')\n",
    "plt.ylabel('Rel-Perm')\n",
    "plt.title('Wylie-Gardner Rel-Perm Model')\n",
    "\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2. Pirson's Correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_p = pd.DataFrame(data=sw, columns=['Sw'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_p['Sw*'] = (df_p['Sw'] - Swc)/(1-Swc)\n",
    "\n",
    "df_p['Krw'] = np.sqrt(df_p['Sw*'])*df_p['Sw']**3\n",
    "\n",
    "df_p['Kro'] = (1 - df_p['Sw*'])*np.sqrt(1 - (df_p['Sw*']**0.25)*np.sqrt(df_p['Sw']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sw</th>\n",
       "      <th>Sw*</th>\n",
       "      <th>Krw</th>\n",
       "      <th>Kro</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.250000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.254545</td>\n",
       "      <td>0.006061</td>\n",
       "      <td>0.001284</td>\n",
       "      <td>0.921328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.259091</td>\n",
       "      <td>0.012121</td>\n",
       "      <td>0.001915</td>\n",
       "      <td>0.900600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.263636</td>\n",
       "      <td>0.018182</td>\n",
       "      <td>0.002471</td>\n",
       "      <td>0.884430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.268182</td>\n",
       "      <td>0.024242</td>\n",
       "      <td>0.003003</td>\n",
       "      <td>0.870372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>0.681818</td>\n",
       "      <td>0.575758</td>\n",
       "      <td>0.240506</td>\n",
       "      <td>0.224779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.686364</td>\n",
       "      <td>0.581818</td>\n",
       "      <td>0.246636</td>\n",
       "      <td>0.219870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.690909</td>\n",
       "      <td>0.587879</td>\n",
       "      <td>0.252875</td>\n",
       "      <td>0.215002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.695455</td>\n",
       "      <td>0.593939</td>\n",
       "      <td>0.259225</td>\n",
       "      <td>0.210173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.600000</td>\n",
       "      <td>0.265687</td>\n",
       "      <td>0.205386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Sw       Sw*       Krw       Kro\n",
       "0   0.250000  0.000000  0.000000  1.000000\n",
       "1   0.254545  0.006061  0.001284  0.921328\n",
       "2   0.259091  0.012121  0.001915  0.900600\n",
       "3   0.263636  0.018182  0.002471  0.884430\n",
       "4   0.268182  0.024242  0.003003  0.870372\n",
       "..       ...       ...       ...       ...\n",
       "95  0.681818  0.575758  0.240506  0.224779\n",
       "96  0.686364  0.581818  0.246636  0.219870\n",
       "97  0.690909  0.587879  0.252875  0.215002\n",
       "98  0.695455  0.593939  0.259225  0.210173\n",
       "99  0.700000  0.600000  0.265687  0.205386\n",
       "\n",
       "[100 rows x 4 columns]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3NzcYGBigWrVqWL9+vQo6JSIiopJCreEmNTUVrq6uWLt2baHqY2Ji0LVrV7i7u+PmzZvw9vbG5MmTcfDgQSV3WrDYt7E49scxLDuxDEOCh8BtsRuysrPU2hMREdHnGDFiBHr37i0xduDAARgYGGD58uVq6qpw1Hq1VJcuXdClS5dC169fvx729vYICAgAADg5OeHatWtYsWIF+vbtq6w2P2lQ8CBcfHJRYuzxq8f4ovIXauqIiIhIsYKDgzFx4kQEBgZizJgxUsuzsrI++/40ilKiLgW/dOkSOnbsKDHWqVMnbN68GWKxWOZlY5mZmcjMzMz/Pjk5GcA/Z7Ar6k6RztbOUuHmVuwt1KpUSyGvr2p5n0tZuJNmScD50CycD82jyXMiFoshCAJyc3ORm5ur7naKRBCE/N5//PFHLFiwADt27EDfvn2Rm5uLkSNHIikpCU2aNMHatWuhp6eHZ8+e4fbt25g8eTKuXr0KIyMjfPXVV1i5ciXKlSv3yW3m5uZCEASIxWJoa2tLLCvK/JaocJOQkAArKyuJMSsrK2RnZyMxMRE2NjZS6/j7+2PhwoVS46dOnVLcpXnvpYeOnD+Ccq8/PZGaLDw8XN0t0L9wPjQL50PzaOKc6OjowNraGh8/fkRW1j+nK9T3r48P6R/U1pOZoRlued36ZJ1YLEZ2djamTZuGzZs3Y8+ePWjTpo3EToKzZ8/C0NAQBw8ezL8Tc9euXdGwYUOcOXMGiYmJmDx5MsaPH49169Z9cptZWVlIT09HVFQUsrOzJZalpaUV+j2WqHADSF8mJgiCzPE8Xl5emDZtWv73ycnJsLOzQ8eOHWFqaqqQnoz/NMame5skxjKNMtG1a1eFvL6qicVihIeHw8PD47NuokSKwfnQLJwPzaPJc5KRkYG//voL5cqVg4GBAQAgOSMZSenqexSDSCQq1N8/XV1dnD59GmFhYQgPD0e7du2klhsbGyM0NDT/cNSmTZuQkZGBoKAgWFtbQyQSQUtLC7169cLKlSuldlD8V0ZGBgwNDdGqVav8zytPXqgqjBIVbqytrZGQkCAx9vr1a+jo6Mi986O+vj709fWlxnV1dRX2S1Dfvr7U2P34+xr3S1ZUivyM6PNxPjQL50PzaOKc5OTk5P+BV8QDIRWlML2IRCLUq1cPiYmJ8PX1RZMmTWBiYiKxvG7duhIh5NGjR3B1dYWxsXH++3Z3d0dubi4eP34s8wjLf/sSiUQy57Ioc6s5n3QhNGvWTGq346lTp9CwYUO1/kBbmljC2sxaYuzpm6dIyyz8LjQiIiJNU7lyZURGRiI+Ph6dO3dGSkqKxHJjY2OJ7wVBkHskRZU3MlTrnpuPHz/iyZMn+d/HxMTg1q1bsLCwgL29Pby8vPDy5Uts27YNADB+/HisXbsW06ZNw9ixY3Hp0iVs3rwZu3fvVtdbyOdi64KED//bqyQIAh4kPICbg5sauyIiIk1jbmReorZvb2+PyMhItG3bFh07dsTJkyflHtZydnbG1q1bkZqaml9z8eJFaGlpoVYt1V1ko9Zwc+3aNbRt2zb/+7xzY4YPH47Q0FDEx8cjNjY2f7mjoyPCwsLg6emJwMBA2NraYvXq1Wq9DDyPS2UXnH5wWmLszt93GG6IiEjCM/9n6m6hyKpUqYKIiAiJgCPL4MGDsWDBAkyYMAGLFy/G27dv8f3332Po0KGfPN9GkdQabtq0aZN/QrAsoaGhUmOtW7fGjRs3lNhV8bjYukiN3Y27q4ZOiIiIFC/vEFXbtm3h4eEBW1tbqRojIyOcOHEC33//PZo0aQIjIyP07dsXq1atUmmvJeqEYk3mUllGuHnJcENERCWTrB0MNjY2ePjwYYHr1a1bF0ePHoWpqanaTqIuUScUazJnW2epMYYbIiIi1WO4URATAxNUrVBVYuxl0ku8T5Vxhz8iIiJSGoYbBapbpa7U2L24e2rohIiIqOxiuFEgmScV89AUERGRSjHcKJDMk4p5xRQREZFKMdwokKxwc+flHTV0QkREVHYx3ChQbava0NaSfET73Zd3C7yXDxERESkWw40C6evqo5aV5O2l36W+k3gsAxERESkXw42C8U7FRERE6sVwo2C8UzEREZF6MdwoWN3K0ve6YbghIqKSZsSIEejdu7fE2IEDB2BgYIDly5erqavCYbhRMF4OTkREpVFwcDAGDx6MtWvXYtasWVLLs7Ky1NCVbAw3ClatYjUY6BpIjN2Lu4fc3Fw1dURERPR5li9fjkmTJmHXrl0YM2YMgP/t2fH394etrS1q1aqFNWvWwNXVNX+9w4cPQyQSITAwMH+sU6dO8PLyUmq/fCq4gmlracPZxhk3Ym/kj6VmpuLF2xdwrOioxs6IiEgT/FztZ2QkZaht+wbmBpjybEqh6+fMmYPAwEAcO3YMHTp0kFh25swZmJqaIjw8HIIgQBAETJkyBW/fvoWpqSkiIyNhaWmJyMhITJw4EdnZ2YiOjoanp6ei35YEhhslcKnsIhFugH9u5sdwQ0REGUkZyHivvnBTFCdOnMCRI0dw5swZtGvXTmq5sbExgoODoaenBwAQBAEVKlTAxYsX4ejoiIiICEyfPh0//fQTAODq1avIyMhAy5Ytldo3D0spAa+YIiKi0qBevXqoWrUq5s+fj5SUFKnldevWzQ82ACASieDu7o4LFy4gKSkJ9+7dw/jx45GTk4MHDx4gIiICDRo0QLly5ZTaN8ONEvBeN0REVBpUrlwZkZGRiI+PR+fOnaUCjrGxsdQ6bdq0wYULF3D+/Hm4urrC3NwcrVq1QmRkJCIiItCmTRul983DUkoga89N9NNoZGVnQU9HT8YaRERUVhiYG3y6SIO2b29vj8jISLRt2xYdO3bEyZMnYWpqKre+devWmDp1Kg4ePJgfZFq3bo3Tp08jOjoaU6YU/nyf4mK4UYIq5augvFF5vE97nz/24u0LLA1bCt+evuprjIiI1K4oJ/NqiipVqiAiIkIi4Mjj4uICCwsL7Nq1C0eOHAHwz96c6dOnA4DSz7cBeFhKKUQiEfo37C817hfmh9t/31ZDR0RERJ8n7xBVUlISPDw8kJSUJLNOJBKhRYsWAAB3d3cA/5y7Y2Zmhi+//LLAvT6Kwj03SrK492IcuHEAbz++zR/LzsnGqNBRuOx1GTra/OiJiEhzhYaGSo3Z2Njg4cOHn1x369atMDU1hZbWP/tQRCIR3r59+4m1FId7bpSkoklFrBm4Rmr8+ovrWBW+Sg0dERERlQ0MN0o0sPFA9HDtITU+/8h8PEp4pIaOiIiISj+GGyUSiUQIGhwEU0PJ44uZ2ZkYvXU0cnJz1NQZERFR6cVwo2SVy1fGqn7Sh6EuPrkIr0PKfbYGERFRWcRwowKjWo5CB6cOUuM/nvwRWy5uUUNHRESkSoIgqLuFEkFRnxPDjQqIRCJsGrYJ5fSlbzc9bvs4RP0ZpYauiIhI2XR1dQEAaWlpau6kZMjKygIAaGtrf9br8HpkFalqWRW7xu5Cr8BeEslUnCPGV0Ff4YrXFVSvVF2NHRIRkaJpa2vD3Nwcr1+/BgAYGRlBJBKpuSvlys3NRVZWFjIyMvIvBS/sem/evIGRkRF0dD4vnjDcqFAP1x5Y3nc5Zh6YKTH+9uNb9FjbA5fmXIKZkZmauiMiImWwtrYGgPyAU9oJgoD09HQYGhoWOchpaWnB3t7+swMgw42KTe84HQ/iHyDkYojE+IP4B+i9rjfCJofBUM9QTd0REZGiiUQi2NjYoFKlShCLxepuR+nEYjGioqLQqlWr/MNyhaWnp1ekvT3yMNyomEgkQtCQIDx580TqXJuIRxHos64Pjkw8An1dfTV1SEREyqCtrf3Z55KUBNra2sjOzoaBgUGRw42i8IRiNdDT0cPB8QdRrWI1qWUn753EgI0DIM4u/emeiIhIGRhu1MTSxBLHvz8Oy3KWUsuO3DqCIZuH8CZ/RERExcBwo0Z1bOog3DMc5kbmUsv2XduHUaGjGHCIiIiKiOFGzerb18fJqSdhYmAitWzbpW0YEjyEh6iIiIiKgOFGAzR2bIywyWEw0jOSWrbn6h58FfQV0rPS1dAZERFRycNwoyFa1myJo5OOQl9H+iqpY7ePodvqbkjJSFFDZ0RERCULw40Gae/UHkcnHZV5n5tzj87BY5UH3qW+U0NnREREJQfDjYbp+EVHnJxyEqaGplLLrsRcgfsP7oh9G6uGzoiIiEoGhhsN5F7LHeemn0OFchWklt2Pv4+m/k1xK/aWGjojIiLSfAw3GqqBQwNEzYyCrbmt1LL4D/Fo9WMrhN8PV0NnREREmo3hRoM52zrj/KzzMu9knJKRgq6ru2Jr9FY1dEZERKS5GG40XLWK1XBpziU0dmwstSw7JxsjtozA3F/mIjc3Vw3dERERaR6GmxKgkmklnJ1+Fj1ce8hc7hfmh34b+iE1M1XFnREREWkehpsSwljfGIe+O4Tv2nwnc/mhG4fQankr/P3ubxV3RkREpFkYbkoQHW0dBA4KhP9X/jKX34i9gcZLG+P3mN9V3BkREZHmYLgpYUQiEeZ0mYOD3x2U+biG+A/xaLW8FUIvhqq8NyIiIk3AcFNCfdXgK5yfdR6VzStLLcvMzsTI0JH4ftf3fOgmERGVOQw3JVgDhwa46nMVjao2krl87bm16PBTB7xOfq3izoiIiNSH4aaEszG3QeTMSHzT+BuZy6P+jILbEjdceXZFxZ0RERGpB8NNKWCoZ4idY3bix69/hJZIekr/fv833Je7Y925dRAEQQ0dEhERqQ7DTSkhEokwo9MM/Db1N1gYW0gtF+eIMXHXRAzdPJT3wyEiolKN4aaU8XD2wDWfa6hXpZ7M5Tuv7ESTpU3wKOGRijsjIiJSDYabUsixoiOi50RjSNMhMpffi7uHhksaYveV3SrujIiISPkYbkopY31jbBu1DesGr4Outq7U8o+ZHzEoeBDGbR+H9Kx0NXRIRESkHGoPN+vWrYOjoyMMDAzg5uaG8+fPF1i/c+dOuLq6wsjICDY2Nhg5ciTevn2rom5LFpFIhO/afIcLsy/A3sJeZs3GqI1o6t+Uh6mIiKjUUGu42bt3L6ZOnQofHx/cvHkT7u7u6NKlC2JjY2XWX7hwAcOGDcPo0aNx79497N+/H1evXsWYMWNU3HnJ0tixMa7PvY5OX3SSufz237fRcElD7Li8Q8WdERERKZ5aw82qVaswevRojBkzBk5OTggICICdnR2CgoJk1l++fBlVq1bF5MmT4ejoiJYtW2LcuHG4du2aijsveSxNLBE2OQx+vf1kXi7+MfMjhm4eiuEhw5GSkaKGDomIiBRDR10bzsrKwvXr1zFnzhyJ8Y4dOyI6OlrmOs2bN4ePjw/CwsLQpUsXvH79GgcOHEC3bt3kbiczMxOZmZn53ycnJwMAxGIxxOKy92iCmR1noqljUwwJGYL4D/FSy7dd2oboJ9H4rs53ZfLz0UR588D50AycD83DOdEsypqPoryeSFDTXd3i4uJQuXJlXLx4Ec2bN88fX7p0KbZu3YpHj2SfA3LgwAGMHDkSGRkZyM7ORs+ePXHgwAHo6kqfNAsAvr6+WLhwodT4rl27YGQk/eDJsiIpMwkBtwJw680tmct1RDoY5jQM3R27y9zTQ0REpEppaWkYNGgQPnz4AFNT0wJr1R5uoqOj0axZs/xxPz8/bN++HQ8fPpRa5/79++jQoQM8PT3RqVMnxMfHY+bMmWjUqBE2b94sczuy9tzY2dkhMTHxkx9OaZebm4sfT/0I32O+yMnNkVnj4eSB4GHBsDGzUXF3lEcsFiM8PBweHh5yQzypDudD83BONIuy5iM5ORmWlpaFCjdqOyxlaWkJbW1tJCQkSIy/fv0aVlZWMtfx9/dHixYtMHPmTABAvXr1YGxsDHd3dyxZsgQ2NtJ/gPX19aGvry81rqury18CAHN7zEV75/b4ZtM3ePH2hdTy8AfhcPNzQ8iIEPRw7aGGDikPf2Y1C+dD83BONIui56Mor6W24w16enpwc3NDeHi4xHh4eLjEYap/S0tLg5aWZMva2toAwGcmfYZm1Zvh1vxb6OfWT+byxI+J6Lm2JybsnIC0zDQVd0dERFQ0aj2ZYtq0aQgODmcL2pMAACAASURBVEZISAgePHgAT09PxMbGYvz48QAALy8vDBs2LL++R48eOHToEIKCgvDs2TNcvHgRkydPRuPGjWFra6uut1EqmBuZY++4vdg4dCOM9GSfixQUEYQGSxrg+ovrKu6OiIio8NQabgYMGICAgAAsWrQI9evXR1RUFMLCwuDg4AAAiI+Pl7jnzYgRI7Bq1SqsXbsWLi4u6NevH2rXro1Dhw6p6y2UKiKRCGNbjcUVryuoZlZNZs2jhEdo6t8Ufsf9kJ2TreIOiYiIPk1t59zkmTBhAiZMmCBzWWhoqNTY999/j++//17JXZVtta1q44cWP+Cy+DJWnV4ldcgvOycbcw/PRdidMGwbtQ3VK1VXU6dERETSeI0vyaSrpQv/Pv447Xkalc0ry6yJfhoN10Wu2Bi1kec8ERGRxmC4oQK1c2qH27630b9hf5nLUzNTMW77OHRb3Q3xSdI3BSQiIlI1hhv6JAtjC+z5dg+2j94OU0PZ9xY4cfcEXHxdsO/qPhV3R0REJInhhgpFJBJhSNMhuLPgDtrUbiOz5l3qOwzYOAADNgxAYkqiahskIiL6fww3VCT2FexxZtoZrOy3Evo60jdHBIB91/bBxdcFR24dUXF3REREDDdUDFpaWpjWcRpuzLuBBvYNZNa8Sn6F3oG9MWzzMLxPfa/iDomIqCxjuKFic7Z1xmWvy1jQYwG0tbRl1my/vB0uvi44fvu4irsjIqKyiuGGPouuji58e/ristdlONs4y6yJS4pD9zXdMTxkOPfiEBGR0jHckEI0rNoQ1+ddx6xOs6Alkv1jte3SNnyx4Av8+sevKu6OiIjKEoYbUhgDXQP88PUPuDD7AmpWqimzJv5DPHqu7YkhwUPw9uNbFXdIRERlAcMNKVzeU8aneUyDSCSSWbPzyk44z3fG/mv7eXdjIiJSKIYbUgojfSOs7L8SF2ZdQC2rWjJrXqe8Rv8N/dE3qC/vbkxERArDcENK1bxGc9yafwvTO06Xuxfnl5u/wHmBM7Zc3MK9OERE9NkYbkjpDPUMsaLfClycfRFONk4ya5LSkjAqdBQ6/tQRz948U3GHRERUmjDckMo0q94MN+bdgHdXb7n3xTn94DTq+tbFT+E/ISc3R8UdEhFRacBwQyploGsAvz5+uOpzFa5VXGXWpGWlYdq+aWi+rDlu/31bxR0SEVFJx3BDavGl/Ze46nMVfr395D6j6veY3+G2xA3eh7yRnpWu4g6JiKikYrghtdHV0YV3N2/cmn8LLWu0lFmTnZMN/xP+cF3oiohHEaptkIiISiSGG1K7OjZ1EDkzEoGDAlFOv5zMmsevH6PtirYYHToa71LfqbhDIiIqSRhuSCNoaWlhQtsJuL/oPrrX6y63LuRiCJzmOWHXlV28bJyIiGRiuCGNYmdhh6OTjmLvt3tRyaSSzJrXKa8xOHgwOgd05mXjREQkheGGNI5IJEL/Rv3xYPEDjGoxSm7dqfun8MWCL7DsxDKIs8Uq7JCIiDQZww1pLAtjC2wesRnnZpyT+wiHDHEGvA554cvFX+Lik4sq7pCIiDQRww1pvDa12+CPBX9gXvd50NXWlVlzL+4eWv7QEmO3jeUJx0REZRzDDZUIBroGWNRrUYGXjQNA8Plg1JlXB9uit/GEYyKiMorhhkoUZ1tnRM6MRPCwYJQ3Ki+z5k3KGwzfMhxtV7TFg/gHKu6QiIjUjeGGShwtLS2Mdh+Nh4sfYmjToXLrIv+MhOtCV3gf8kZaZpoKOyQiInViuKESq5JpJWwbvQ2np51GzUo1ZdaIc8TwP+GPLxZ8gWN/HFNxh0REpA4MN1TitXdqj9u+t+Hbwxd6Onoya56/fY4ea3ugd2BvvHj7QsUdEhGRKjHcUKlgoGuABT0X4K7vXXRw6iC37sitI3Ca7wT/MH9kZWepsEMiIlIVhhsqVWpa1cQpz1PYNWYXrM2sZdakZ6XD+xdv1FtYD6fvn1Zxh0REpGwMN1TqiEQifNPkGzxc9BCT20+Glkj2j/mjhEfw+MkDAzYMwMv3L1XcJRERKQvDDZVaZkZm+Hngz7g29xqaODaRW7fv2j7Unlcby39bzkNVRESlAMMNlXpf2n+J6DnR2Dh0IyyMLWTWpGamYvbB2XBd6IozD86ouEMiIlIkhhsqE7S0tDC21Vg8WvwIY93Hyq17mPAQHVZ1QP/1/fHXu79U2CERESkKww2VKZYmltg4bCMue11GA/sGcuv2X9+POvPqYOnxpcgUZ6qwQyIi+lwMN1QmNanWBL/7/I7AQYEwNzKXWZOWlQafwz5w8XXB8dvHVdwhEREVF8MNlVnaWtqY0HYC/lzyJ0a3HC237snrJ+i+pju6r+6OJ6+fqLBDIiIqDoYbKvMqmlRE8PBgXPa6DDcHN7l1x+8cxxcLvoDXIS98zPiowg6JiKgoGG6I/l+Tak1wxfsKNgzdIPeqqqzsLCw7sQy159XGriu7IAiCirskIqJPYbgh+hdtLW182+pbPPZ7jAltJsi9AWBcUhwGBw9Gq+WtcDP2poq7JCKigjDcEMlgYWyBwMGBuD73OlrUaCG37sKTC3Bb4oZvt32LNylvVNghERHJw3BDVID69vVxftZ57Bi9AzZmNjJrBEHApvObUNOnJgJOB0CcLVZxl0RE9G8MN0SfIBKJMLjpYDxa8ghzusyBrrauzLoP6R/gudcT9RbWw8m7J1XcJRER5WG4ISokEwMT+H/lj3sL76F7ve5y6x4mPETnnzujx5oe+DPhTxV2SEREAMMNUZHVtKqJX7//FWGTw1DLqpbcumO3j8HF1wXT901HUlqSCjskIirbGG6IiqlL3S6443sHK/qtgImBicwacY4Yq8JXodbcWtgQuQE5uTkq7pKIqOxhuCH6DHo6epjecToe+z3GGPcxEIlEMuvepLzB+B3j0WBxA5x9cFbFXRIRlS0MN0QKYGVqhU3DNuGazzW0rNFSbt3tv2+j/ar26BPYh49yICJSEoYbIgVq4NAAUbOisOfbPbC3sJdbd/jWYTjPd8aM/TN4Pg4RkYIx3BApmEgkwoBGA/Bw8UMs6rUIRnpGMuvEOWKsPLUSNX1qYt25dcjOyVZxp0REpRPDDZGSGOoZYl73efhzyZ8Y2nSo3LrEj4mYuGsi6i2shxN3TqiwQyKi0onhhkjJKpevjG2jt+GK9xU0r95cbt2D+AfourorOgd0xt2Xd1XYIRFR6cJwQ6QijR0b48LsC588H+fkvZNwXeiKcdvH4VXyKxV2SERUOjDcEKnQv8/H8evth3L65WTW5Qq52Bi1ETW8a2DZb8uQmZOp4k6JiEouhhsiNTDUM4R3N+9P3h/nY+ZHzD86HxPPTcTOKzuRm5ur4k6JiEoetYebdevWwdHREQYGBnBzc8P58+cLrM/MzISPjw8cHBygr6+P6tWrIyQkREXdEimWtZk1Ng3bhJvzbqK9U3u5dYkZiRi5dSQaL22MiEcRqmuQiKgEUmu42bt3L6ZOnQofHx/cvHkT7u7u6NKlC2JjY+Wu079/f5w5cwabN2/Go0ePsHv3btSpU0eFXRMpnqudK8I9w/HrpF9Rx1r+z/P1F9fRdkVb9FrbCw/jH6qwQyKikkOt4WbVqlUYPXo0xowZAycnJwQEBMDOzg5BQUEy63/77TdERkYiLCwMHTp0QNWqVdG4cWM0by7/ChSikkIkEqG7a3fcXnAbawethWU5S7m1R/84ChdfF0zYOQGvk1+rsEsiIs2no64NZ2Vl4fr165gzZ47EeMeOHREdHS1znaNHj6Jhw4ZYvnw5tm/fDmNjY/Ts2ROLFy+GoaGhzHUyMzORmfm/kzGTk5MBAGKxGGKxWEHvpnTJ+1z4+ajPty2/Rf8G/bHst2VYe24tsnKypGpycnMQFBGE7Ze2Y2bHmZjSforcGwaS4vD3Q/NwTjSLsuajKK+ntnCTmJiInJwcWFlZSYxbWVkhISFB5jrPnj3DhQsXYGBggF9++QWJiYmYMGEC3r17J/e8G39/fyxcuFBq/NSpUzAy4h+CgoSHh6u7hTKvlUEr1G5dGzse7sD5ONnno33M/IgFvy7A6vDVGFR7ENpUaQNtkbaKOy17+PuheTgnmkXR85GWllboWpEgCIJCt15IcXFxqFy5MqKjo9GsWbP8cT8/P2zfvh0PH0qfT9CxY0ecP38eCQkJMDMzAwAcOnQIX3/9NVJTU2XuvZG158bOzg6JiYkwNTVVwjsr+cRiMcLDw+Hh4QFdXV11t1Pm5c1H+Vrl4X3EGxefXiyw3sXWBf59/NHRuaPcq7Co+Pj7oXk4J5pFWfORnJwMS0tLfPjw4ZN/v9W258bS0hLa2tpSe2lev34ttTcnj42NDSpXrpwfbADAyckJgiDg77//Rs2aNaXW0dfXh76+vtS4rq4ufwk+gZ+RZmlWoxnOzz6PwzcPY/bB2Xj8+rHMurtxd9EjsAfaO7XH8r7L0cChgYo7LRv4+6F5OCeaRdHzUZTXUtsJxXp6enBzc5PabRUeHi73BOEWLVogLi4OHz9+zB/7888/oaWlhSpVqii1XyJNIBKJ0KdBH9xbeO+TJx2feXAGbkvcMHjTYMS8iVFhl0RE6qXWq6WmTZuG4OBghISE4MGDB/D09ERsbCzGjx8PAPDy8sKwYcPy6wcNGoQKFSpg5MiRuH//PqKiojBz5kyMGjVK7gnFRKWRro4uJradiKdLn8K7qzcMdA3k1u76fRfqzK8Dz72eePvxrQq7JCJSD7WGmwEDBiAgIACLFi1C/fr1ERUVhbCwMDg4OAAA4uPjJe55U65cOYSHhyMpKQkNGzbE4MGD0aNHD6xevVpdb4FIrUwNTeHXxw+PlzzGyBYj5Z5jk5WdhYDTAajmXQ3+Yf5Iyyz8iXlERCWN2s65yTNhwgRMmDBB5rLQ0FCpsTp16vCMeKL/qGJRBSEjQjC1w1TMPjgbv939TWZdcnoyvH/xxtpza7Gw50KMaD4COtpq/2eAiEihivWvmiAIOHDgAM6dO4fXr19LPe/m0KFDCmmOiIqmXpV6ODHlBE7fP43ZB2fjRuwNmXVxSXEYu20sVp5aCf+v/NGrfi9eWUVEpUaxDktNmTIFQ4cORUxMDMqVKwczMzOJLyJSrw7OHXDV5yp2jdkFR0tHuXUPEx6iz7o+aPFDC5z/s+DnuhERlRTF2nOzY8cOHDp0CF27dlV0P0SkIFpaWvimyTf4qsFXWB+5HouPL5Z7QvGlp5fQ6sdW6Fa3G/y/8kfdKnVV3C0RkeIUa8+NmZkZqlWrpuheiEgJ9HX1MaXDFDz1ewqfrj4w1JN/ZeHxO8fhusgVw0OG43nic9U1SUSkQMUKN76+vli4cCHS09MV3Q8RKYmZkRmW9FmCJ35PMK7VOGhryX5EgyAI2HZpG2rPq42pe6bywZxEVOIUK9z069cP79+/R6VKlVC3bl00aNBA4ouINJetuS3WD12PewvvoW+DvnLrsrKz8POZn1Hduzp8j/oiJSNFhV0SERVfsc65GTFiBK5fv44hQ4bAysqKV1kQlUC1rWvjwHcHcOXZFcw5NAcRjyJk1n3M/IiFvy5E4LlAeHf1xndtvivwpoFEROpWrHBz/PhxnDx5Ei1btlR0P0SkYk2qNcHZ6Wdx8t5JzDk4B3/8/YfMusSPiZi2bxp+Ov0TfHv4YlizYbxHDhFppGIdlrKzs+MTtYlKEZFIhM4unXFj3g3sGrML1SrKv2Dgr3d/YfTW0ajrWxcHrh+Qus8VEZG6FSvcrFy5ErNmzcLz588V3A4RqVPe5eMPFj3AusHrYG1mLbf2YcJD9FvfD438GuHk3ZMQBEGFnRIRyVescDNkyBCcO3cO1atXh4mJCSwsLCS+iKhk09PRw3dtvsMTvydY2mcpzAzl35zzRuwNdP65M9qsaIMLjy+osEsiItmKdcA8ICBA0X0QkQYy1jeGV1cvjGs9Dst/W47VZ1cjPUv2LSCi/oyC+3J3dK3bFUt6L8GX9l+quFsion8UOdyIxWJERERg3rx5vJEfURlhYWyBZX2XYXL7yVh8bDGCLwQjOydbZm3YnTCE3QlDP7d+WNRrEerY1FFxt0RU1hX5sJSuri5++eUXZfRCRBrO1twWQUOC8HDRQwxpOqTA20Dsv74fXyz4AiNCRiDmTYwKuySisq5Y59z06dMHhw8fVnQvRFRCVK9UHdtHb8cf8/9Ar/q95NblCrnYemkras+rjQk7J+Dl+5cq7JKIyqpinXNTo0YNLF68GNHR0XBzc4OxsbHE8smTJyukOSLSbHWr1MXhiYdx5dkV+Bz2wZkHZ2TWiXPECIoIwpaLWzChzQTM7jwblUwrqbhbIiorihVugoODYW5ujuvXr+P69esSy0QiEcMNURnTpFoTnJ52GmcfnIXPYR9cfnZZZl2GOAOrwldhQ9QGTG43GTM6zYCFMa+wJCLFKla4iYnh8XMiktbOqR2i60Tj2O1jmHd4nty7HadmpsL/hD8CIwIxrcM0eHp4wtSQNwYlIsUo1jk3ebKysvDo0SNkZ8u+aoKIyh6RSIQerj1wY94N7P12L2pb15Zbm5yeDN9ffeHo5YhlJ5bhY8ZHFXZKRKVVscJNWloaRo8eDSMjI3zxxReIjY0F8M+5NsuWLVNog0RUMmlpaaF/o/6463sXoSNDUbVCVbm171LfweuQF6p5V8PKUyuRlpmmukaJqNQpVrjx8vLCH3/8gYiICBgY/O/pwB06dMDevXsV1hwRlXw62joY3nw4Hi15hPVD1qOyeWW5tW9S3mDG/hmo7lMdq8+sRoY4Q4WdElFpUaxwc/jwYaxduxYtW7aUuM+Fs7Mznj59qrDmiKj00NPRw7jW4/Bk6RP8PPBnWJlaya1N+JCAKXumoIZ3Daw7tw6Z4kwVdkpEJV2xws2bN29QqZL0ZZypqakF3tSLiMhA1wCT20/G06VPsfzr5ahQroLc2pdJLzFx10TUnFsTGyI3ICs7S4WdElFJVaxw06hRIxw/fjz/+7xAs2nTJjRr1kwxnRFRqWasb4yZnWYixj8GS3ovgbmRudzav979hfE7xqPW3FoIPh8McbZYhZ0SUUlTrHDj7+8PHx8ffPfdd8jOzsbPP/8MDw8PhIaGws/PT9E9ElEpZmJgAp9uPojxj8H87vMLvCT8xdsXGLttLGrPq42QCyEMOUQkU7HCTfPmzREdHY20tDRUr14dp06dgpWVFS5dugQ3NzdF90hEZYC5kTkW9lqIGP8Y+HT1QTn9cnJrYxJjMHrraNSZXwdbLm6R+xBPIiqbihxuUlJSEB4ejtjYWKxcuRJ3797F/fv3sWPHDtStW1cZPRJRGWJhbIElfZYgxj8GszrNgpGekdzaZ2+eYVToKNSZVwehF0MZcogIQBHDze3bt1GnTh107twZ3bt3R40aNXD69Gll9UZEZZiliSV++PoHxPjHYHrH6TDUM5Rb+/TNU4wMHcmQQ0QAihhu5syZA3t7e5w/fx7Xrl1D69atMWnSJGX1RkSESqaVsKLfCjxb+gyeHTxhoGsgtzYv5NSeVxtbLm7hOTlEZVSRws21a9ewZs0aNG/eHA0aNEBISAgeP36Mjx95y3QiUi5rM2usGrAKMf4xmNphaoEhJ+9wVe15tbH5/GaGHKIypkjhJjExEfb29vnfV6hQAUZGRnjz5o3CGyMiksXazBo/DfgJz5Y++2TIiUmMwZhtY1Bzbk1sjNrI++QQlRFFCjcikQgpKSlITk5GcnIyPnz4IDWWnJysrF6JiPLZmNvkh5wp7acUGHJevH2BcdvHoYZPDQRFBPGOx0SlXJHCjSAIqFWrFsqXL4/y5cvDwsICHz9+xJdffony5cvD3Nwc5cuXV1avRERSbMxtEDAwoFB7cv569xcm7JyA6t7VsebMGqRnpauwUyJSFZ2iFJ87d05ZfRARfZa8PTmzO8/G8t+WY33Uernh5WXSS0zeMxlLTyzFzI4zMa71OBjrG6u4YyJSliKFm9atWyurDyIihcg78Xh2l9lYcXIF1kWsQ1pWmszahA8JmL5/Opb9tgzTPaZjQtsJMDEwUXHHRKRoxbpD8b9169YN8fHxiuiFiEhhrEyt8GO/HxHjH4PZnWcXuGfmTcobzDk0B1XnVMXiY4uRlJakwk6JSNE+O9xERUUhPZ3HrYlIM1UyrYRlfZfhuf9z+HT1KXDPzLvUd5h/ZD4c5jhg3uF5SExJVF2jRKQwnx1uiIhKAksTSyzpswTPlz3Hgh4LYGZoJrc2OT0ZS44vQVWvqpi5fyYSPiSosFMi+lyfHW4cHBygq6uriF6IiJTOwtgCvj198WLZCyzutRgWxhZya1MzU7Hi1Ao4ejli0q5JiH0bq8JOiai4Pjvc3L17F3Z2dorohYhIZcyMzDC3+1w8X/YcP/T9AZVMKsmtzRBnIPBcIKr7VMe3279F3Mc4FXZKREVV6Kulbt++XegXrVevXrGaISJSNRMDE8zqPAuT2k7CxvMb8ePJHxGXJDu8ZOdkI/RSKLZhGyI/RmJu97lwqeyi4o6J6FMKHW7q168PkUgEQRBkLs9bJhKJkJOTo7AGiYhUwUjfCFM7TMV3rb/DlotbsOy3ZXjx9oXM2lzkYu+1vdh7bS961e8F767eaOzYWMUdE5E8hQ43MTExyuyDiEgj6OvqY3yb8RjdcjR2XNkB/zB/PH79WG79kVtHcOTWEXRw6gCfbj5oXas1RCKRCjsmov8qdLhxcHBQZh9ERBpFV0cXI1uMxLBmw7D/2n74hfnh7su7cutPPziN0w9Oo1n1ZvDu4o1u9box5BCpSbFPKN6+fTtatGgBW1tbvHjxz67bgIAAHDlyRGHNERGpm7aWNgY2Hog/5v+BwxMPw83ercD6S08vocfaHqi/qD52X9mN7JxsFXVKRHmKFW6CgoIwbdo0dO3aFUlJSfnn2JibmyMgIEChDRIRaQItLS30qt8L0bOj4dvEF61qtiqw/vbftzEoeBDqzKuDjVEb+SRyIhUqVrhZs2YNNm3aBB8fH2hra+ePN2zYEHfu3FFYc0REmkYkEqF+xfo47XkaF2ZfQNe6XQusf/rmKcZtHwdHL0esOLkCKRkpKuqUqOwqVriJiYnBl19+KTWur6+P1NTUz26KiKgkaFGjBY5PPo6b826if8P+BZ5jE/8hHjMPzITDbAfMPzIfb1LeqLBTorKlWOHG0dERt27dkho/ceIEnJycPrspIqKSpL59fewdtxcPFz3E6Jajoast/67t79PeY/GxxXCY44DJuyfLvdyciIqvWOFm5syZmDhxIvbu3QtBEPD777/Dz88PXl5emDVrlqJ7JCIqEWpZ10Lw8GA8XfoUU9pPgZGekdza9Kx0rDm7BtW9q2PY5mEFXolFREVTrHAzcuRILFiwALNmzUJaWhoGDRqE9evXY82aNXB3d1d0j0REJYqdhR0CBgbgxbIXmNd9HsyNzOXW5uTmYPvl7ajrWxc91vTAhccXVNgpUelU7EvBx44dixcvXuD169dISEjA77//jps3b6JGjRqK7I+IqMSyNLHEol6LEPtDLH78+kfYmtsWWH/s9jG4L3dHi2UtcPTWUeTm5qqoU6LSpUjhJikpCYMHD0bFihVha2uL1atXw8LCAoGBgahRowYuX76MkJAQZfVKRFQimRiYYEanGXi29Bk2DduEmpVqFlgf/TQavQJ7oa5vXYReDEVWdpZqGiUqJYoUbry9vREVFYXhw4fDwsICnp6e6N69O86fP4+wsDBcvXoV33zzjbJ6JSIq0fR19THGfQweLH6AfeP2oYF9gwLr78ffx8jQkajmVQ0rT61EcnqyijolKtmKFG6OHz+OLVu2YMWKFTh69CgEQUCtWrVw9uxZtG7dWlk9EhGVKtpa2ujXsB+uzb2GcM9wtHdqX2D9y6SXmLF/Buxn28PrkBfik+JV1ClRyVSkcBMXFwdnZ2cAQLVq1WBgYIAxY8YopTEiotJOJBKhg3MHnJ52Gld9ruJrt68LvFfOh/QPWHZiGap6VcXYbWPxKOGRCrslKjmKFG5yc3Ohq/u/+zdoa2vD2Nj4sxpYt24dHB0dYWBgADc3N5w/f75Q6128eBE6OjqoX7/+Z22fiEgTNKzaEPvH78ejxY8wrtU46Ovoy63Nys5C8PlgOM13Qu/A3rj45KIKOyXSfIV+KjgACIKAESNGQF//n1+6jIwMjB8/XirgHDp0qFCvt3fvXkydOhXr1q1DixYtsGHDBnTp0gX379+Hvb293PU+fPiAYcOGoX379nj16lVR3gIRkUaraVUT64euh29PX6w+sxrrItbhQ/oHmbWCIODIrSM4cusImlVvhpkdZ6Jn/Z7Q1tKWWU9UVhRpz83w4cNRqVIlmJmZwczMDEOGDIGtrW3+93lfhbVq1SqMHj0aY8aMgZOTEwICAmBnZ4egoKAC1xs3bhwGDRqEZs2aFaV9IqISw9rMGku/Woq/lv+Flf1Wokr5KgXWX3p6CV8FfQWneU7YELkB6VnpKuqUSPMUac/Nli1bFLbhrKwsXL9+HXPmzJEY79ixI6Kjowvs4enTp9ixYweWLFmisH6IiDSRiYEJpnWchkntJmHP73uw/ORy3Iu7J7f+8evHGL9jPOYenotJbSdhQtsJqGhSUYUdE6lfkcKNIiUmJiInJwdWVlYS41ZWVkhISJC5zuPHjzFnzhycP38eOjqFaz0zMxOZmZn53ycn/3MppVgshlgsLmb3pVve58LPRzNwPjSLuuZDBBG+afQNBjYciN/u/YZV4asQ+ThSbn3ix0T4/uqLZb8tw9AmQzGl/RTUsqqlwo5Vh78jmkVZ81GU11NbuMnz3ysDBEGQebVATk4OBg0ahIULF6JWrcL/gvr7+2PhwoVS46dOnYKRkfznvhAQHh6u7hboXzgfmkXd8+FZ2xM9rHrg0NNDuBx/GbmQfTfjDHEGNl3YhOALwWhk1Qi9ORECUgAAIABJREFUqvWCs4VzgVdllVTqnhOSpOj5SEtLK3StSBAEQaFbL6SsrCwYGRlh//796NOnT/74lClTcOvWLURGSv6PJCkpCeXLl4e29v9OlMvNzYUgCNDW1sapU6fQrl07qe3I2nNjZ2eHxMREmJqaKuGdlXxisRjh4eHw8PCQuDqO1IPzoVk0cT6eJT7D6jOrEXopFGlZn/4D0NChIaa2n4qvvvwKOtpq/z/uZ9PEOSnLlDUfycnJsLS0xIcPHz7591ttP9V6enpwc3NDeHi4RLgJDw9Hr169pOpNTU1x584dibF169bh7NmzOHDgABwdHWVuR19fP//qrn/T1dXlL8En8DPSLJwPzaJJ81HbpjYChwRiUe9FWB+5HqvPrMbrlNdy66+9uIYhIUPgUMEBU9pPweiWo2FqWPL/s6dJc0KKn4+ivFaxH5ypCNOmTUNwcDBCQkLw4MEDeHp6IjY2FuPHjwcAeHl5YdiwYf80qqUFFxcXia9KlSrBwMAALi4un32/HSKikq5CuQrw6eaDFz+8wKZhm1DHuk6B9S/evsC0fdNgN9sOM/bPQOzbWBV1SqRcag03AwYMQEBAABYtWoT69esjKioKYWFhcHBwAADEx8cjNpa/bERERWGga4Ax7mNwb+E9HPv+GNrUblNgfXJ6MlaeWolq3tUwcONA/B7zu2oaJVIStYYbAJgwYQKeP3+OzMxMXL9+Ha1atcpfFhoaioiICLnr+vr64tatWyrokoio5NHS0kK3et1wbsY5XJt7DYMaDyrwBn85uTnYe3UvmixtgpY/tMShG4eQk5ujwo6JFEPt4YaIiJTPzcENO8fuRIx/DGZ0nPHJc2wuPrmIvkF9UdOnJn4+/TNSMlJU1CnR52O4ISIqQ+ws7PBjvx/x1w9/4acBP8GhgkOB9TGJMZi6dyqqzKqC6fum43nic9U0SvQZGG6IiMogU0NTTO0wFU/8nmDfuH1o4tikwPrk9GSsCl+F6t7V8XXQ17j45CLUdCcRok9iuCEiKsN0tHXQr2E/XPa+jOg50ejn1g9aIvl/GnKFXBy8cRAtf2iJxn6NsfPyTmRlZ6mwY6JPY7ghIiIAQLPqzbBv/D48XfoUnh08YWJgUmD9tRfXMGTzEFSdUxVLji3Bm5Q3KuqUqGAMN0REJKGqZVWsGrAKfy//Gz8N+AmOlv/X3p3HRV3nfwB/DQz3fckNonIoiJp4oJlWiqWtZZlupWVqm1nterZabWr9SnNdtXazY/NIc9XcMnWTFTYDD8QQD1QURJD7PodrDub7+2MERYlzLmZeTx/z+H7ny/fznffwYZzX43t92r5JarPC6kL85dBf4PuWL+bvnI+UvBQtVUrUNoYbIiJqU/N5OTc+vIHvX/se4wLHtbu+VCHF9tPbMWTtEDy88WH8eOFHXkpOOsFwQ0RE7TI1McXTDzyNE2+dQNI7SZg9ejbMTNu/FX5cWhymb52OAW8PwN9i/oaq+iotVUvEcENERF0Q0TcCu+fvxq31t/Du1Hfhauva7vq3ym9h+YHl8F7hjUV7FuFa4TUtVUrGjOGGiIi6zMvRCx889QFyPs7B1y9+jcHeg9tdv15Wj8/jPseg9wZh8ubJ+CnlJyiVSi1VS8aG4YaIiLrNytwK88fNx6XVl3B82XFMGzINIpGo3TYxqTF44u9PIOjdIGz53xZU11drqVoyFgw3RETUYyKRCA+HPIxDbxxCxocZWDJxSYdDPNwsvYkl+5fA+y3VIavUglQtVUuGjuGGiIjUqp9bP2yatQn5G/Lxj+f/gSD3oHbXr5PW4fO4zxG6OhQTN03EoYuHeJUV9QjDDRERaYStpS1ef/h1XHv/Gv77p/9iyuApHbb5+drPeOqzp9D/7f74OPpjlEnKtFApGRqGGyIi0igTExNMDpuMn/74E9I+SMMfH/1jh3c/zi7PxsofVsLnLR+8vONlJGcna6laMgQMN0REpDVBHkH45PefIG9DHv7+3N8R7BHc7vpShRQ7E3Yi4v8iELkuEnsS90Aql2qpWuqtGG6IiEjr7K3s8cYjbyB1bSqOLT6GJ8Kf6PAqq8TMRMzeNht+f/bDOwffQW5Frpaqpd6G4YaIiHTGxMQEUaFROPLmEWR8mIFlUcvgaO3YbpsSSQk+OvoR+q7si+mfTcfP13+GIAhaqph6A4YbIiLSC/3c+mHjsxuRvyEf/3zxnwj3CW93faWgxI8Xf8Tjnz6ON+LewN+P/53DPBAAhhsiItIz1hbWWDBuAS6+dxEnVpzArBGzIDYVt9smvy4fy/69DN4rvPHKrldwIeeClqolfcRwQ0REekkkEmFc0Djs+8M+ZK/PxurfrYaHg0e7bepl9fj65Nd44IMHELkuErsSdqFR3qiliklfMNwQEZHe83L0wpppa5CzPgf7/7AfDwU91GGbxMxEvLTjJfi85YMVB1bgZslNLVRK+oDhhoiIeg0zsRlmjpiJ+BXxuLzmMl6b8BpsLWzbbVNeW46NMRsx4J0BeGzLY/jxwo9QNCm0VDHpAsMNERH1SmHeYdj6wlbc+ugW/hD2Bwz0HNhhm2NXj2H61unou7Iv1h5ei4KqAi1UStrGcENERL2avZU9pvSdgovvXkTc8jjMjJjZ8QnIVflYc2QN/P7sh6e3Po2YqzFQKpVaqpg0jeGGiIgMgkgkwvjg8dj/6n7kfpyLD578AL7Ovu22aVI24eCFg5i8ZTIC3w3Ex9Efo6SmREsVk6Yw3BARkcHxcPDAu0+8i8yPMnHo9UN4LOyxDu+AnFma2TKe1awvZ+H4teO8OWAvxXBDREQGS2wqxrSh0xD9p2hkfJiBPz/2Z7jaurbbRt4kx3fnvsOjmx5F8LvB2HhsI0cn72UYboiIyCj0c+uH9c+sR96GPOxZsKdTl5PfKLmBFf9eAe+3vPHcV88hLi2Oe3N6AYYbIiIyKhZmFnh+1POIXxGPq2uv4o+P/hEOVg7ttpEpZNiXtA8Pb3wYIX8JwcZjG1EqKdVSxdRVDDdERGS0BnkNwie//wQFfy3A9rnbMSpgVIdt0ovTVXtzVnjj91/9Hj9f+5lXWukZhhsiIjJ61hbWeHnsy0h8OxEX37uI1ya8BjtLu3bbyJvk2J+0HxM3TUTQu0FYH70eRdVFWqqY2sNwQ0REdJchvkOw9YWtKPhrAb5+8WuMDBjZYZubpTex6odV8P2zL57e+jSiL0ejSdmkhWqpLQw3REREbbC1tMX8cfNx9u2zuPCXC53am6NoUuDghYOY8ukUBKwKwJrDa5Bdnq2liqkZww0REVEHhvoNbdmbs+2lbZ06Nye3Ihdrj6xFwKoAPLblMfw7+d+QKWRaqJYYboiIiDrJ1tIW8x6ch8S3E3Fp9SW88fAbHV5pJQgCjl09hme/eBbeK7yx7LtlSC1I1VLF2qdUKFEZX4m6kjqd1cBwQ0RE1A3hPuH4+/N/R+HGQuyatwvjAsd12KastgybYjchdHUoxqwfg20nt0HSKNFCtZqnkCqQ/FUyvgj7Atmbs5H0aZLOamG4ISIi6gErcyvMiZyDE2+dwLX3r2FZ1DK42bl12O7MzTNYsGsBPJd7Yt7OeTidcbpX3iBQVivDmU1n8Gm/T/GfV/+DqswqAEDyF8lorGrUSU0MN0RERGoS4hmCjc9uRN6GPBxYeACTQyd3OKZVnbQOO07vwIMfP4iB7w3Ehv9u6BWXlDdUNCD+g3hs6bsFMctiIClovQdKWiNF0lbd7L1huCEiIlIzc7E5Zgyfgf8u/i+y1mVh9e9WdzhCOQCkFaXhz9//GT5v+WDaP6bhxws/Qq6Qa6HizqvJq8GxZcew2W8z4t6LQ0N5w2+um7Q1CUqF9m9wKNb6KxIRERkRfxd/rJm2Bn954i/4X+r/8PWpr3Ho4iHIm347tDQpm3Dk0hEcuXQEfez6YPbo2Xh57MsI8w7TYuWtlV0vw+kNp5HybQqU8vYDi8hchIiFEXhwxYMwEWt/PwrDDRERkRaYmphicthkTA6bjFJJKb5N/BbbTm3D1YKr7bYrkZRgU+wmbIrdhAj/CLw89mU8N/I5ONk4aaXunNM5SNiQgLTDaR2ua+FggYhFEagOqcak5ybBzMxMCxXej+GGiIhIy9zs3LBk0hIsnrgYSbeSsO3UNuz9dW+HV06dyz6Hc9nnsPS7pXhq2FOYO2YuJg2aBFMTU7XWJygFpB1JQ8KGBOQm5Ha4vk0fG4xeOhojXhsBEysTHD16VK31dBXDDRERkY6IRCKMDBiJkQEjsXnmZnx//nvsOL0Dv6T90m47qUKK/Un7sT9pP7wcvfBi5It4KfIlhHiG9KgeeYMcl3ZdQuKmRJSnl3e4vmOAI8asGIOhc4fCzEq1l0Yu1/05Qgw3REREesDawhpzIudgTuQcZJZmYsfpHfjmzDfIrWh/z0lBVQHWR6/H+uj1GBUwCnPHzMWsEbO6dNiqrrQOSVuTkPSPJNSX1Xe4vnu4O8auHIvQZ0N1ck5NRxhuiIiI9Ew/t3744KkPsGbaGhy/fhw7Tu/AD+d/gFQhbbfd2ayzOJt1Fov3L8a0IdPw0piXMDl0MsSmbX/dl6aWInFLIlJ2p0DRqOiwrr4T+mLMijEY8PiADi9x1yWGGyIiIj1lamKKSYMmYdKgSaisq8S+pH3YmbATv2b92m47qUKKA8kHcCD5ANzt3fHCqBcwd8xcDPYZDEEQkPm/TCRuTkRGdEaHNYhMRBj4zECMWTEG3iO81fXWNIrhhoiIqBdwsnHCaxNew2sTXkNqQSp2JuzE7sTdHd7wr7imGJtiN+HT6E8xtXwqhqcMhzK743vPiK3EGPryUEQuiYTzAGd1vQ2tYLghIiLqZQZ5DcKGGRvw0fSPEJMag52nd+LQpUNtjjpuV2eHEakjEHE9AtZSayjRfrCx6WODkW+ORMTCCFi7WmvoHWgWww0REVEvJTYVY8rgKZgyeAoq6iqwP2m/6rBV5q/wLfHFqKujMDBrIEyFji8Vtx5gjUdWPIIhLw6B2LJ3x4PeXT0REREBAJxtnPHK6FcwJmcM4vfHozKlslPtMnwycCbsDG5634R/pj9mR8/G7NGze3xZuS4x3BAREfVy1TnVOPfFOZz/+jzqSzu+lFtuKkfKgBScDT2LEueSluXZ5dn48OiH+PDoh4jwj8Ds0bPx+5G/h7u9uybLVzuGGyIiol5IEARkHc9C0mdJSDuUBkEpdNjG1MUUGSMzcMD1AOot2g9BzXdDXnZgGaIGRWH26Nl4cuiTsLGwUddb0BiGGyIiol6ksaoRF7+5iHOfn0N5Wsd3EQYA71HeGPnmSIQ+GwpTc1O8X/4+9pzdg11nduF60fV22zYpmxB9JRrRV6JhY2GDp4c9jRdGvYBHBz76m/fP0TX9rIqIiIhaKTxfiKTPk3B5z2UoGjq+4Z6JmQnCZoVh5Jsj4T2y9f1p/Fz8sGrKKqx8fCWSs5OxO3E39v66F6WS0na3WSetw+7E3diduBvu9u6YNWIWXhj1Akb0HaFXN/VjuCEiItJTsjoZruy7guQvklFwrqBTbey87DD81eEY/ofhsPWwbXddkUiEiL4RiOgbgY0zNiImNQa7E3fj0MVDaJQ3ttu2uKYYn/78KT79+VME9gnE86Oex/Mjn0eAS0Cn35+m6HxAiK1btyIgIACWlpYYPnw4Tp48+Zvr/vDDD5g0aRLc3Nxgb2+PyMhIHDt2TIvVEhERaV5xSjGOvnEUm7w24ciCI50KNv7j/THjuxn4060/Yfx74zsMNvcyE5thavhU7PvDPhRtLMK2l7bhkZBHOrVH5kbJDaw9shbBfwlG5PpIHM48jMLqwi69vjrpdM/N/v37sXjxYmzduhVjx47Fl19+iccffxypqanw8/O7b/0TJ05g0qRJ+Oijj+Do6IgdO3bgd7/7Hc6ePYthw4bp4B0QERGph6xOhqv7ryL5q2Tkn83vVBtzW3OEzwlHxGsRcB+sviuaHKwdMO/BeZj34DzkVeRhX9I+7E7cjZS8lA7bJuckIxnJ2Pn2TsyMmIm9f9irtro6S6fhZtOmTZg/fz4WLFgAANiyZQuOHTuGzz//HOvWrbtv/S1btrR6/tFHH+HQoUM4cuQIww0REfVKhecLcf7r87i85zKkNe0PjNnMLdQNIxaNQPjscFjYW2i0Ph9nHyyfvBzLJy/Hlfwr2HN2D/ac3dPhaOVKQQkXWxeN1vZbdBZuZDIZkpOTsXLlylbLo6KikJCQ0KltKJVKSCQSODv3rjEviIjIuDVWNeLyvy7j/NfnUXSh/bGhmpmam2LQjEEY/upw+I3z08kJvGHeYVj39Dp8+NSHOJVxCnvO7sGBcwdQWd/2DQOfH/m8litU0Vm4KSsrQ1NTE9zdW+9Gc3d3R1FR5zr6b3/7G+rq6jBz5szfXEcqlUIqvZOEa2pqAAByuRxyubwblRu+5t8Lfz/6gf2hX9gf+qe39ImgFJB9IhuXdlxC2sE0KBo7vuIJAJz6O2HYK8MQ/mJ4y1hPCkXn2mpSZEAkIgMisWnGJhxLPYZ9SftwJOVIy4nI/s7+iPCLUFu/dGU7Or9a6t7kKQhCp9Lo3r17sWbNGhw6dAh9+vT5zfXWrVuHtWvX3rc8JiYG1ta9c0AwbYmNjdV1CXQX9od+YX/oH33tE1mpDBXHK1BxvAKy4vsHtmyLSCyCwygHuES5wHawLSpMKhD3a5xmC+0BU5jiBc8X8LTb00gsSsSJ/BMIdAxEdHS02l6jvr7jOy8301m4cXV1hamp6X17aUpKSu7bm3Ov/fv3Y/78+Thw4AAmTpzY7rqrVq3C0qVLW57X1NTA19cXUVFRsLe37/4bMGByuRyxsbGYNGkSzMzMdF2O0WN/6Bf2h/7Rxz6R18uR9mMaUnan4NbxW0DHNw8GADgPcMbQ+UMxeM5g2PTR/zsBt2WafBpiY2MxceJEmJubq227zUdeOkNn4cbc3BzDhw9HbGwspk+f3rI8NjYWTz755G+227t3L+bNm4e9e/di6tSpHb6OhYUFLCzuP9nKzMxMbz4E+oq/I/3C/tAv7A/9o+s+EQQBuadzcfGbi7i6/ypkks7tpRFbijHo2UF4YMEDOjuXRhPMzc3V2h9d2ZZOD0stXboUc+bMQUREBCIjI/HVV18hJycHCxcuBKDa65Kfn49du3YBUAWbF198EZ988glGjx7dstfHysoKDg4OOnsfRERkvCqzKnFp1yWk7EpBZWbnRuIGAM8HPDF03lCEvxAOS0dLDVZofHQabmbNmoXy8nK8//77KCwsRFhYGI4ePQp/f38AQGFhIXJyclrW//LLL6FQKPD666/j9ddfb1n+0ksvYefOndoun4iIjFRDZQNS/52KlN0pyDmZ03GD26ycrTB49mAMe3kYPIZ6aLBC46bzE4oXLVqERYsWtfmzewNLXFyc5gsiIiJqQ5OsCTeibyBldwrSj6SjSdbUqXYiExH6T+6PoXOHIvjJYIgtdP7Va/D4GyYiIvoNglJAzqkcpOxJQeqBVDRWtj/e0t1cQ1wx9OWhCJ8dDjsvOw1WSfdiuCEiIrqLIAgoTinGlb1XcGXvFVTnVHe6raWTJcKeC8OQF4fAe6S3wZwc3Nsw3BAREQGoyKjA5b2XcWXvFZRdK+t0OxOxCQKnBGLIS0MQODWQh530AHuAiIiMVnVONa5+dxVX91/t1Mjbd/MZ7YPBswcjbFZYy52DST8w3BARkVGpya/Bte+v4er+q8hNaH/wx3s59XfC4BcGI3x2OFwCdTMoJHWM4YaIiAyepECC1O9TkfpdKnJO53T6jsEAYNPHBqG/D0X4C+HwGuHF82h6AYYbIiIySNW51bj2wzVc+/e1LgcaCwcLDHx6IMKeC0PAwwEwEZtorlBSO4YbIiIyGJVZlS2BJi8xr0ttxVZiBD0RhMHPD8aAxwZAbMmvyN6KPUdERL1aaWopir4rwrY121B8sbhLbU3NTRE4JRChs0IR9EQQzG3VN9Aj6Q7DDRER9SqCUkB+Uj6uH7yO6z9eR3laeZfam5iZYMDkARg0cxCCpwXD0oHjOhkahhsiItJ7TbImZP2ShbRDaUg7lAZJgaRL7U3MTNA/qj9CZ4aqAg0HqjRoDDdERKSXGiobkBGdgbRDabgRfQMyiaxL7U0tTBH4eCAGzhiIoCeCuIfGiDDcEBGR3qi4WYG0w2lIP5KO7BPZEJq6cIkTADMbMwRNDULI0yEInBIICzsLDVVK+ozhhoiIdEapUCI3IRfpP6Uj/Uh6l4Y9aGblbAXLIZaY+OZEBD0exKuciOGGiIi0q76sHhnHMnDjpxvIiM5AY1XnR9puZu9rj5CnQhAyPQReo73w35j/InBKIMRm/FojhhsiItIwQSmg8EIhbhy9gYyjGcg7m9elG+o1cx/ijuBpwQh+MhieD3i23ClYLperuWLq7RhuiIhI7erL63Ez5iYyojNw89hN1JXUdXkbJmIT+I/3R9DvghDyZAgc+zpqoFIyRAw3RETUY0qFEvm/5iPjmCrMFCQVQFB2ffeMpZMlAqcEIuh3QRjw2ABe4UTdwnBDRETdUplViczYTNyMuYnM/2VCWi3t1nbcQt0Q9EQQAqcGwjfSl+M4UY8x3BARUac0VjXiVtwt3Iy9icyYTFRkVHRrO2JLMQIeCcCAKQMQOCUQTgFOaq6UjB3DDRERtUkhVSAvMQ+ZsZnI/F9mtw81AYBTfycMeGwAAqcGou+EvjCzMlNztUR3MNwQEREAQNmkROH5QmT9nIWs41nIOZUDRYOiW9sSW4kR8HAA+j/WH4GPB8J5gLOaqyX6bQw3RERGSlAKKL5cjFu/3ELW8Sxkn8ju9nkzANAnrA/6T+6PAY8NgN+DfryZHukM//KIiIyEoBRQcqUEt+JuITs+G7fib6GhvKHb27PpY4N+E/uhX1Q/9JvYD/be9mqslqj7GG6IiAyUskmJ4kvFuBV/CzkncpB9IhsNFd0PM2IrMfwf8kfAowHoP6k/3MPdITIRqbFiIvVguCEiMhAKqQIFSQXIPpmNnJM5yDmV0+WRtO8mMhXBe4Q3+j7SF/0m9oPvGF+ILfi1QfqPf6VERL1UQ2UD8s7kIedUDnJO5iA/KR9N0qYebdM93F0VZh7tB79xfryJHvVKDDdERL2AIAiozKxEbkIuck+rHiVXSnq8XdeBruj7cF8EPBKAvuP7wtrVuufFEukYww0RkR6SN8hRmFyI3DO5yEvIQ25CbrfGZ7qXW6gb/Mf7o++EvvB/yB+27rZqqJZIvzDcEBHpmCAIqMqqQt7ZPOSdUT2KLhZBqVD2bMMiwGOoB/wf8of/Q/7wG+cHGzcb9RRNpMcYboiItKyhsgEFSQXI/zUfeYl5yD+bj/qy+h5v19TcFF4jvOA3zg/+4/zhO8YXlo48Z4aMD8MNEZEGyRvkKLpQhPyk/JZAU3Gje2My3cvS0RK+Y33hO9YXfmP94D3SmzfOIwLDDRGR2iikCpRcLkFBcgEKzhWgIKkAJVdKIDR1bzyme7kEucB3jC98In3gO9YXbgPdeJ8ZojYw3BARdYOiUYHSS6UoSC5A4flCFCYXojilGEp5D8+Tuc3M2gzeI73hPdobvpGqQMPzZYg6h+GGiKgD0hopii4VoehCEQqSC5B+Ih0peSk9P+H3Lq4hrvAe5Q3vUaow0yesD0zEJmrbPpExYbghIrpNEARI8iUouliEootFKL5UjKKLRajIUM85Ms1s+tiogsxI1cNrhBesnKzU+hpExozhhoiMkrxBjtLUUhRfKkZxSnHLtCdjL7XFwt4CnsM94TXCC14RXvAe6Q0HPweIRDxXhkhTGG6IyKApm5SoyqpC8eVilFwuQcnlEhSnFKMiowKCUj0n+jYztzWHxzAPeEV4qQJNhBdcAl140i+RljHcEJFBEAQB1TnVKL1aipKrJarplRKUppZC0aBQ++tZ2FvA8wFPeDzgAc8HPOH5gCdcglxgYsrzZIh0jeGGiHoVQSmgKrsKpamlKE0tRVlqWcu8rLb7I2C3x8bdRhVkhnnAbbAbrlddx1MvPwVzC3ONvB4R9QzDDRHpJXmDHBU3KlCWVoaya7cf18tQllamkT0xACAyEcEl2AUeQz3gPsQdHkM94DHEA7Yed8ZfksvlyDqaxUNNRHqM4YaIdKb56qTy9HKUpZWhPK0c5Wmq+apbVYB6T4lpxdrVGu7h7ugzuA/ch7jDPdwdboPcYGZlprkXJSKtYLghIo0SBAH1ZfWoyKhAxY0KlKeXozy9XDV/oxzyOrlGX19sJUaf0D7oE9YHbmFucA93h/tgd9i42/CKJSIDxXBDRD0mCAJqC2tRcbMClTcrUZGhmpbfKEdFRgWk1VKN12BqYQrXEFf0Ce0Dt1A3uIW6oU9oHzgGOPIkXyIjw3BDRJ0ib5Cj6lYVKjMrUZVVhYqbFajKVE0rMys1dh7MvcxszOAa4gq3QW6tHgwxRNSM4YaIAABNsiZU51aj6lYVqrKqWk0rsypRW1ir1XpsPW3hGuIK1xBXuAS7wG2gG1wHusLex56Hk4ioXQw3REZCWiNFdW41qrOrUZVdheoc1Xzzc0mBRKMn8LbFzNoMzoHOcA12hXOQauoS5AKXYBdYOlhqtxgiMhgMN0QGQNGoQE1eDWryalCdW42a3LumOdWozqnWynkvbTG1MIXzAGfVI9AZLoEucAlygXOgM+y87LgXhojUjuGGSI8JgoDGqkY05DQgMyYT9cX1qMmvgSRfAkm+pCXQ1JfV67ROcztzOPd3hlN/JzgPuDN17u+sOozEe8IQkRYx3BDpgCAIkFZLISmUoLawFpJCCSQFt+cLJK0ezSfqpiFNZ/WKTERw8HOAY4AjnPo5tUyd+zvDqZ8TrFysuAeGiPQGww2RGslqZagtrkVdcd2daVGtar5INS8plKC2qBZN0iZdl3uHCLD3sYejvyMc/G+HmAAnOPZ1hGObWdhEAAAP+UlEQVSAI+x97GFqZqrrKomIOoXhhqgdCqkC9WX1qC+tR11pHepK6lTzJXVtPjR9Q7ruEluJ4eDnAAdfBzj4O6jmb08d/W+HF3OGFyIyDAw3ZDSaZE1oqGhQhZXyejSUN9yZltW3ftwOMzKJZgZiVCdTc1PY+9jDztsODr4OsPe1Vz187FVhxs+Bh42IyKgw3FCvIggCZLUyNFY2oqGyoWXaUHF7vqJBtbxCNV9fXq9aVt6gsRGjNcnK2Qq2nrZoNGtEwJAAVXjxVgUZe29ViLF2tWZwISK6C8MNaZVSoYS0RorG6kZIq1tPG6vuma+SorFKNd9Q2dAyLzRp+WYsGmDtZg1bD1vYedrB1sMWtp62sPOyU0097VrmzazMIJfLcfToUUyZMgVmZhzUkYioIww31KEmWRNktTLIamWQSqSQSVrPSyVSSGvuzMtqZJDWSNt8yOv185wUdbBytoKNuw1s3W1h427TMm/roXrc/TOenEtEpDkMNwZC2aSEokEBWZ0M8no55HVyyOvlqud1bUxrZZDVqUJK8/PmqVQiRXVZNdKa0iCrlaFJpkdX9WiRpaMlrN2sYe1qDRs3G1i7WcOmz52pjZsqwNj0sYG1qzUDCxGRntB5uNm6dSv++te/orCwEKGhodiyZQvGjRv3m+vHx8dj6dKluHr1Kry8vPDWW29h4cKFWqy46wRBgKJR0bL3Q1bbOoA0P1qCyT0PRYOi9bI22mnismI5DGQviwiwcrKClbMVrFysYO1irZq6Wrc8t3azVk1drVuWM6wQEfVOOg03+/fvx+LFi7F161aMHTsWX375JR5//HGkpqbCz8/vvvWzsrIwZcoUvPLKK/j2229x+vRpLFq0CG5ubnjmmWd08A5U8n/NR/HlYtX9TIru3M+ktqgWdSV1kNXKICh7/3kiumZuaw5LR0tYOlnC0tESVk5WqnmnO/PWLtaqEHP70bwuR4smIjIeOg03mzZtwvz587FgwQIAwJYtW3Ds2DF8/vnnWLdu3X3rf/HFF/Dz88OWLVsAAAMHDsS5c+ewceNGnYabpM+ScGnXJZ29fm9gamEKSwdLmNuZw9LBEhYOFi3T5nlLx9bLrZysVGHm9nLuSSEios7QWbiRyWRITk7GypUrWy2PiopCQkJCm23OnDmDqKioVssmT56Mbdu2QS6Xt3kliVQqhVR6Z8DAmpoaAIBcLodcrp7DLlZuVmrZjl4xUe0pMbc1h7nN7amd+Z1ldz23sLdoPW9vDgtb1dTcTrVMbNGzPzUllFDKlWp6c71L89+puv5eqWfYH/qHfaJfNNUfXdmezsJNWVkZmpqa4O7u3mq5u7s7ioqK2mxTVFTU5voKhQJlZWXw9PS8r826deuwdu3a+5bHxMTA2tq6B+/gjpLKErVsp8tMARMLE9XD0gQm5renbS2zvGvZ7amppWnr5VZ3lonMRR3eO0V2+18talv/oOb2o0Bj79woxcbG6roEugv7Q/+wT/SLuvujvr7zAwTr/ITie79ABUFo90u1rfXbWt5s1apVWLp0acvzmpoa+Pr6IioqCvb29t0tu5Wrkqs4tP1Qmz9rPuzSvPfDzNYM5tbmMLMxUz2szWBmdWdebC2GmZUZxFZimNuYq55bm8HM8q71bVQ/19RhGrlcjtjYWEyaNIn3VdED7A/9wv7QP+wT/aKp/mg+8tIZOgs3rq6uMDU1vW8vTUlJyX17Z5p5eHi0ub5YLIaLi0ubbSwsLGBhYXHfcjMzM7X90n1G+GD86vEtN2Nrvq+JrbstxJY6z4/dps7fEfUc+0O/sD/0D/tEv6i7P7qyLZ1985qbm2P48OGIjY3F9OnTW5bHxsbiySefbLNNZGQkjhw50mpZTEwMIiIidPoH7RrsiglrJujs9YmIiOgOnV4fu3TpUnz99dfYvn07rl27hiVLliAnJ6flvjWrVq3Ciy++2LL+woULkZ2djaVLl+LatWvYvn07tm3bhuXLl+vqLRAREZGe0ekxk1mzZqG8vBzvv/8+CgsLERYWhqNHj8Lf3x8AUFhYiJycnJb1AwICcPToUSxZsgSfffYZvLy88Omnn+r0MnAiIiLSLzo/IWTRokVYtGhRmz/buXPnfcvGjx+P8+fPa7gqIiIi6q1421YiIiIyKAw3REREZFAYboiIiMigMNwQERGRQWG4ISIiIoPCcENEREQGheGGiIiIDArDDRERERkUhhsiIiIyKDq/Q7G2CYIAoGtDpxsbuVyO+vp61NTUcIRdPcD+0C/sD/3DPtEvmuqP5u/t5u/x9hhduJFIJAAAX19fHVdCREREXSWRSODg4NDuOiKhMxHIgCiVShQUFMDOzg4ikUjX5eilmpoa+Pr6Ijc3F/b29roux+ixP/QL+0P/sE/0i6b6QxAESCQSeHl5wcSk/bNqjG7PjYmJCXx8fHRdRq9gb2/P/yj0CPtDv7A/9A/7RL9ooj862mPTjCcUExERkUFhuCEiIiKDYrpmzZo1ui6C9I+pqSkmTJgAsdjojlzqJfaHfmF/6B/2iX7RdX8Y3QnFREREZNh4WIqIiIgMCsMNERERGRSGGyIiIjIoDDdERERkUBhujNTWrVsREBAAS0tLDB8+HCdPnvzNdU+dOoWxY8fCxcUFVlZWCAkJwebNm7VYreHrSn/c7fTp0xCLxRg6dKiGKzQuXemPuLg4iESi+x7Xr1/XYsWGraufD6lUinfeeQf+/v6wsLBA//79sX37di1Vaxy60idz585t8zMSGhqquQIFMjr79u0TzMzMhH/+859Camqq8Kc//UmwsbERsrOz21z//Pnzwr/+9S/hypUrQlZWlrB7927B2tpa+PLLL7VcuWHqan80q6qqEvr16ydERUUJQ4YM0VK1hq+r/fHLL78IAIS0tDShsLCw5aFQKLRcuWHqzudj2rRpwqhRo4TY2FghKytLOHv2rHD69GktVm3YutonVVVVrT4bubm5grOzs7B69WqN1chwY4RGjhwpLFy4sNWykJAQYeXKlZ3exvTp04XZs2eruzSj1N3+mDVrlvDuu+8Kq1evZrhRo672R3O4qays1EZ5Rqer/REdHS04ODgI5eXl2ijPKPX0O+TgwYOCSCQSbt26pYnyBEEQBB6WMjIymQzJycmIiopqtTwqKgoJCQmd2saFCxeQkJCA8ePHa6JEo9Ld/tixYwdu3ryJ1atXa7pEo9KTz8ewYcPg6emJRx99FL/88osmyzQa3emPw4cPIyIiAhs2bIC3tzeCgoKwfPlyNDQ0aKNkg6eO75Bt27Zh4sSJ8Pf310SJAIxw4ExjV1ZWhqamJri7u7da7u7ujqKionbb+vj4oLS0FAqFAmvWrMGCBQs0WapR6E5/3LhxAytXrsTJkyd5N1Y1605/eHp64quvvsLw4cMhlUqxe/duPProo4iLi8NDDz2kjbINVnf6IzMzE6dOnYKlpSUOHjyIsrIyLFq0CBUVFTzvRg168h0CAIWFhYiOjsa//vUvTZUIgOHGaIlEolbPBUG4b9m9Tp48idraWiQmJmLlypUYMGAAnnvuOU2WaTQ62x9NTU14/vnnsXbtWgQFBWmrPKPTlc9HcHAwgoODW55HRkYiNzcXGzduZLhRk670h1KphEgkwp49e1pGkN60aRNmzJiBzz77DFZWVhqv1xh05zsEAHbu3AlHR0c89dRTmioNAMON0XF1dYWpqel9CbukpOS+JH6vgIAAAMDgwYNRXFyMNWvWMNz0UFf7QyKR4Ny5c7hw4QLeeOMNAKr/zAVBgFgsRkxMDB555BGt1G6IevL5uNvo0aPx7bffqrs8o9Od/vD09IS3t3dLsAGAgQMHQhAE5OXlITAwUKM1G7qefEYEQcD27dsxZ84cmJuba7JMXgpubMzNzTF8+HDExsa2Wh4bG4sxY8Z0ejuCIEAqlaq7PKPT1f6wt7fH5cuXcfHixZbHwoULERwcjIsXL2LUqFHaKt0gqevzceHCBXh6eqq7PKPTnf4YO3YsCgoKUFtb27IsPT0dJiYm8PHx0Wi9xqAnn5H4+HhkZGRg/vz5mixRRWOnKpPear6Mb9u2bUJqaqqwePFiwcbGpuXM9ZUrVwpz5sxpWf8f//iHcPjwYSE9PV1IT08Xtm/fLtjb2wvvvPOOrt6CQelqf9yLV0upV1f7Y/PmzcLBgweF9PR04cqVK8LKlSsFAML333+vq7dgULraHxKJRPDx8RFmzJghXL16VYiPjxcCAwOFBQsW6OotGJzu/p81e/ZsYdSoUVqpkYeljNCsWbNQXl6O999/H4WFhQgLC8PRo0dbzlwvLCxETk5Oy/pKpRKrVq1CVlYWxGIx+vfvj/Xr1+PVV1/V1VswKF3tD9KsrvaHTCbD8uXLkZ+fDysrK4SGhuKnn37ClClTdPUWDEpX+8PW1haxsbF48803ERERARcXF8ycORP/93//p6u3YHC6839WdXU1vv/+e3zyySdaqVEkCIKglVciIiIi0gKec0NEREQGheGGiIiIDArDDRERERkUhhsiIiIyKAw3REREZFAYboiIiMigMNwQERGRQWG4ISIiIoPCcENEvUpJSQleffVV+Pn5wcLCAh4eHpg8eTLOnDmj69KISE9w+AUi6lWeeeYZyOVyfPPNN+jXrx+Ki4vx888/o6KiQtelEZGe4PALRNRrVFVVwcnJCXFxcRg/fvx9P1+2bBnS09Nx5MgRAMCWLVuwZMkS/Oc//8HUqVMBAMHBwVi6dCnHRiMyYDwsRUS9hq2tLWxtbfHjjz9CKpXe9/MJEybg5MmTUCqVAID4+Hi4uroiPj4eAFBUVIT09PQ2gxERGQ6GGyLqNcRiMXbu3IlvvvkGjo6OGDt2LN5++22kpKQAAB566CFIJBJcuHABgiDg5MmTWLZsGeLi4gAAv/zyC9zd3RESEqLDd0FEmsZwQ0S9yjPPPIOCggIcPnwYkydPRlxcHB544AHs3LkTDg4OGDp0KOLi4nD58mWYmJjg1VdfxaVLlyCRSH7zcBYRGRaGGyLqdSwtLTFp0iS89957SEhIwNy5c7F69WoAqkNTcXFxiI+Px/jx4+Hk5ITQ0FCcPn0acXFxmDBhgm6LJyKNY7ghol5v0KBBqKurA3DnvJvjx4+3BJnx48dj3759PN+GyEjwaiki6jXKy8vx7LPPYt68eQgPD4ednR3OnTuHN998E1OnTsW2bdtQXV0NZ2dniEQiXLp0CaGhoTh06BCeeeYZODs7o6SkRNdvg4g0jPe5IaJew9bWFqNGjcLmzZtx8+ZNyOVy+Pr64pVXXsHbb78NAHBwcMCwYcOQk5ODQYMGAQDGjRsHpVLJvTZERoJ7boiIiMig8JwbIiIiMigMN0RERGRQGG6IiIjIoDDcEBERkUFhuCEiIiKDwnBDREREBoXhhoiIiAwKww0REREZFIYbIiIiMigMN0RERGRQGG6IiIjIoDDcEBERkUH5f5ucvnKnh80zAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('default')\n",
    "\n",
    "plt.plot(df_p['Sw'] , df_p['Kro'], lw=3.5,label ='Kro',color='darkgreen')\n",
    "plt.plot(df_p['Sw'] , df_p['Krw'], lw=3.5,label='Krw', color='purple')\n",
    "\n",
    "# plt.xlim(0,1)\n",
    "\n",
    "plt.xlabel('Sw')\n",
    "plt.ylabel('Rel-Perm')\n",
    "plt.title('Pirsons Rel-Perm Model')\n",
    "\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 3 : Corey's Model\n",
    "\n",
    ">Use Corey’s approximation to generate the gas-oil relative permeability for a formation with a connate water saturation of 0.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "sg = np.linspace(0.05,0.70,100)\n",
    "\n",
    "swc = 0.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "sg_star = sg/(1-swc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "kro = (1-sg_star)**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "krg = sg_star**3 * (2 - sg_star)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sg, krg,label='Krg',lw=3.5,color='darkblue')\n",
    "plt.plot(sg,kro,label='Kro',lw=3.5,color='darkgrey')\n",
    "\n",
    "\n",
    "plt.xlabel('Sg')\n",
    "plt.ylabel('Rel-Perm')\n",
    "plt.title('Coreys Rel-Perm Model')\n",
    "\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
